cohtran_appliedmath

Discrete Math



Euler circuits and Euler trails

This set of problems consists of a handful of randomly selected graphs for which the user is to find an Euler circuit or trail (i.e., a walk in the graph that uses every edge exactly once) if it exists. If it does not exist, the user signals this by going on to the next problem. After the problem set is completed, the applet reports how many times the user gave up too soon!

Click on the image below to open this problem set in a new window:

Euler Graphs

The definitions and notation referenced in these applications are from Discrete Mathematics by Doug Ensley and Winston Crawley, published by John Wiley & Sons, 2005.

Back to Discrete Math Mathlets              Back to Mathlets Home

The site www.flashandmath.com is maintained by Doug Ensley (doug@flashandmath.com) and Barbara Kaskosz (barbara@flashandmath.com).
It has been developed with partial funding from the National Science Foundation and the Mathematical Association of America.




Hamiltonian cycles

This set of problems consists of a handful of randomly selected graphs for which the user is to find an Euler circuit or trail (i.e., a walk in the graph that uses every edge exactly once) if it exists. If it does not exist, the user signals this by going on to the next propblem. After the problem set is completed, the applet reports how many times the user gave up too soon!

Click on the image below to open this problem set in a new window:

Hamiltonian Graphs

The definitions and notation referenced in these applications are from Discrete Mathematics by Doug Ensley and Winston Crawley, published by John Wiley & Sons, 2005.

Back to Discrete Math Mathlets              Back to Mathlets Home

The site www.flashandmath.com is maintained by Doug Ensley (doug@flashandmath.com) and Barbara Kaskosz (barbara@flashandmath.com).
It has been developed with partial funding from the National Science Foundation and the Mathematical Association of America.





Planar graphs

This set of problems is similar to the ones on pages 1 and 2, but this time, instead of looking for a particular structure within the graph, the question is whether or not the vertices (nodes) of the graph can be rearranged on the plane so that the edges of the graph do not cross. The user demonstrates an answer of "yes" by actually doing it with a drag-and-drop interface. As before, a negative answer is signaled by giving up.

Click on the image below to open this problem set in a new window:

Planar Graphs

The definitions and notation referenced in these applications are from Discrete Mathematics by Doug Ensley and Winston Crawley, published by John Wiley & Sons, 2005.

Back to Discrete Math Mathlets              Back to Mathlets Home

The site www.flashandmath.com is maintained by Doug Ensley (doug@flashandmath.com) and Barbara Kaskosz (barbara@flashandmath.com).
It has been developed with partial funding from the National Science Foundation and the Mathematical Association of America.



Graph Isomorphism

The simplest way to explain graph isomorphism is to say that one graph can be rearranged to look like the other one. Thanks to a drag-and-drop interface, students can put this notion of isomorphism directly into action. Several problems are given, some that do consist of isomorphic pairs and some that do not.

Click on the image below to open this problem set in a new window:

Isomorphic Graphs

The definitions and notation referenced in these applications are from Discrete Mathematics by Doug Ensley and Winston Crawley, published by John Wiley & Sons, 2005.

Back to Discrete Math Mathlets              Back to Mathlets Home

The site www.flashandmath.com is maintained by Doug Ensley (doug@flashandmath.com) and Barbara Kaskosz (barbara@flashandmath.com).
It has been developed with partial funding from the National Science Foundation and the Mathematical Association of America.










Truth Tables for Expressions Using And, Or & Not

This set of problems consists of a handful of randomly selected expressions for which the user must provide a truth table. The statements use only "and", "or" and "not" as logical connectives and each uses either two or three variables.

Click on the image below to open this problem set in a new window:

TruthTable Basics

The exercises and examples referenced in these applications are from Discrete Mathematics by Doug Ensley and Winston Crawley, published by John Wiley & Sons, 2005.

Back to Discrete Math Mathlets              Back to Mathlets Home

The site www.flashandmath.com is maintained by Doug Ensley (doug@flashandmath.com) and Barbara Kaskosz (barbara@flashandmath.com).
It has been developed with partial funding from the National Science Foundation and the Mathematical Association of America.







 
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